Many methods, devices, apparatus and systems for processing density information of a pixel of a document as well as their applications, for instance in a facsimile system or in a data processing system with a document scanner, have been proposed. A facsimile system is known which executes paper feeding in a predetermined direction called a sub-scanning direction, as described in the Japanese laid-open patent application no. 61-234170 and the Japanese laid-open patent application no. 63-288567. It is also known to increase the number of readings (number of lines) in the sub-scanning direction, as described in "NEFAX 6/60 Facsimile Transceiver", T. Sanpei et al, NEC Technical Report, Vol. 41, No. 9/1988 (page 60 to 62), and in "LSI Architecture of a Facsimile Video Signal Processor, M. Tadauchi et al, 1985 IEEE, 44.1.1-44.1.5 (page 1400-1404). In the facsimile device of the above mentioned prior art, an increased number of scan lines per mm is mentioned. Image processing wherein the resolution degree is improved, is not mentioned. A problem also occurs in that during reading of the succeeding lines, a gap easily occurs between those lines in the sub-scanning direction, so that density information is lost.